46 ON THE EFFECT OF THE INTERNAL FRICTION OF FLUIDS
the differentiation with respect to r rises to the second order, and we get from (70), (75), and (76)
dr*~ rdr r3cZ02~V dt ' We get from this equation and the equations of condition (79)
(dR\ _l(dx\ _l(ffx\ _0 \dr)a~a \de)a a? \.drdd)a ~ '
\rdffa ~ a2 \d02a ~ a dt ~ a '
Hence
Jo, }
......... (97).
We get by integration by parts /^cos 0d0=pasm0—
The first term vanishes at both limits ; and putting for dp/dO its value given by (77), and substituting in (97), we get
or
F= -n-padl .nj-l {aF^ (a) + FJ (a)}
Observing that F,'(d) or Ft(a) = oc - F^a) from (83), and that ^(a) = Aa J, where A is given by (95), and putting M1 for • the mass of the fluid displaced, we get
I I - 2 il ^
which becomes by means of the differential equation (85) which jP3 satisfies
Let
.(99),